Geophys. J. Int. (2021) 224, 2173–2188 doi: 10.1093/gji/ggaa552 Advance Access publication 2020 November 18 GJI Seismology

3-D crustal V S model of western and the surrounding regions using Monte Carlo inversion of seismic noise cross-correlation dispersion diagrams

I. Gaudot,1,* E.´ Beucler ,1 A. Mocquet,1 M. Drilleau,2 M. Haugmard,1 M. Bonnin,1 G. Aertgeerts3 and D. Leparoux4 1Nantes University, University of Angers, Laboratoire de planetologie´ et geodynamique´ UMR-CNRS 6112, 44300 Nantes, France E-mail: [email protected] 2SUPAERO, Institut Superieur´ de l’Aeronautique´ et de l’Espace, 35055 Toulouse, France Downloaded from https://academic.oup.com/gji/article/224/3/2173/5989699 by CNRS user on 15 April 2021 3BRGM, 97300 Cayenne, Guyane France 4 Gustave Eiffel University - IFSTTAR, GERS-GeoEND, Campus Nantes, 44344 Bouguenais, France

Accepted 2020 November 12. Received 2020 October 10; in original form 2020 May 7

SUMMARY Due to a too sparse permanent seismic coverage during the last decades, the crustal structure of western France and the surrounding regions is poorly known. In this study, we present a 3-D seismic tomographic model of this area obtained from the analysis of 2-yr continuous data recorded from 55 broad-band seismometers. An unconventional approach is used to con- vert Rayleigh wave dispersion diagrams obtained from ambient noise cross-correlations into posterior distributions of 1-D VS models integrated along each station pair. It allows to avoid the group velocity map construction step (which means dispersion curve extraction) while providing meaningful VS posterior uncertainties. VS models are described by a self-adapting and parsimonious parametrization using cubic Bezier´ splines. 1268 separately inverted 1-D VS profiles are combined together using a regionalization scheme, to build the 3-D VS model with a lateral resolution of 75 km over western France. The shallower part of the model (hori- zontal cross-section at 4 km depth) correlates well with the known main geological features. The crystalline Variscan basement is clearly associated with positive VS perturbations while negative heterogeneities match the Mesocenozoic sedimentary basins. At greater depths, the Bay of Biscay exhibits positive VS perturbations,which eastern and southern boundaries can be interpreted as the ocean−continent transition. The overall crustal structure below the Armori- can Massif appears to be heterogenous at the subregional scale, and tends to support that both the South-Armorican Shear Zone and the Magnetic Anomaly are major crustal discontinuities that separate distinct domains. Key words: Europe; Inverse theory; Tomography; Crustal imaging; Seismic interferometry; Surface waves and free oscillations.

Armorican Massif, the , the and the Ar- 1 INTRODUCTION dennes, where the pre-Mesozoic basement crops out (Fig. 1a). The The geology of France results from the succession of the Variscan Mesocenozoic episode of extension initiated the formation of the (Palaeozoic) and the (mid-Mesozoic to Paris basin, the and the Southeastern basin, which mid-Cenozoic), punctuated by an intense episode of extensional are the three main sedimentary basins in metropolitan France. From tectonics during the Mesozoic and Cenozoic. According to most 150 to 50 Ma, the counter-clockwise rotation of the Iberian penin- geodynamic models, the Variscan orogeny in western Europe would sula led to the formation of the Bay of Biscay. The Bay of Biscay is a result from the collision of two main continents: Gondwana to the ‘V-shape’ oceanic basin located in southwestern France. The major South and Laurentia- to the North, sandwiching some mi- geological feature of the western France is the , croplates (Armorica, ) separated by oceanic suture (Matte which is a fragment of the Variscan orogeny isolated from the re- 2001;Ballevre` et al. 2009). The French Variscan Massifs are the cent Alpine deformation. The Armorican Massif is divided by two NW–SE oriented Carboniferous shear zones (the North-Armorican Shear Zone and the South-Armorican Shear Zone, hereafter referred ∗ Now at: BRGM, F-45060 Orleans,´ France.

C The Author(s) 2020. Published by Oxford University Press on behalf of The Royal Astronomical Society. All rights reserved. For permissions, please e-mail: [email protected] 2173 2174 I. Gaudot et al.

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Figure 1. (a) Map showing the main geological and structural features of the studied area after Chantraine et al. (2003) and Baptiste et al. (2016). Crystalline basement (AM: Armorican Massif, MC: Massif Central, M: Morvan, IM: Iberian massif, SI: South Ireland, C: Cornwall, B: Black Forest, V: Vosges, ARM: Ardennes-Rhenish massif, P: , A: ), Mesocenozoic sedimentary basins (PB: Paris basin, AB: Aquitaine basin, SB: Southeastern basin, EB:, BCB: Basque-Cantabrian basin, DB: Duero basin, HB: Hampshire basin, WB: Weald basin). Structural features of the western France and surrounding regions (NASZ: North-Armorican Shear Zone, SASZ-N(S): Northern and Southern branch of the South-Armorican Shear Zone, NSE-F: Nort-sur-Erdre fault, EVS: Eo-Variscan suture, PBMA: Paris Basin Magnetic Anomaly, BF: Bray fault, SH: Sillon Houiller, NVF: North Variscan Front, CS: Le Conquet suture, RS: Rheic suture). The dashed black rectangle indicates the western France and the surrounding regions. (b) Location of the 55 seismic broad-band stations used in this study. X7: PYROPE, IB: IBERARRAY, GB: Great-Britain, FR: RLBP, EI: Ireland, G: Geoscope, RD: CEA-LDG. to as SASZ and NASZ, respectively (see Fig. 1a) into three main on the south by the SASZ, and on the east by the Bray fault located domains : (i) the North-Armorican domain, which is a preserved in the Paris basin (Autran et al. 1994). Besides, the geophysical fragment of the (D’Lemos et al. 1990), (ii) the data suggest that the South-Armorican domain, the Massif Central Central- and (iii) the South-Armorican domains which have been af- and the Vosges are closely related (e.g. Baptiste et al. 2016). Using fected by the Variscan orogeny. According to Ballevre` et al. (2009), Lg waves, Campillo & Plantet (1991) detected a NW–SE elongated the SASZ would be a major discontinuity which separates Armor- region of attenuating material in the Central-Armorican domain, ica related (including the Central- and North-Armorican which is correlated with a zone of strong seismic heterogeneity in domains) from Gondwana related terranes (including the South- the crust (Matte & Hirn 1988). Arroucau et al. (2006) observed Armorican domain). that old Variscan regions display a lower attenuation than young The geology of the Armorican Massif and the surrounding Alpine regions. More recently, the low frequency (1 Hz) absorp- regions have been extensively studied during the last century tion tomography results of Mayor et al. (2017) showed that the (Chantraine et al. 2003). The development of geophysical exper- Mesocenozoic basins are associated with high absorption regions, iments in the early 1970s provided images of the structures at whereas the Variscan regions are characterized with low absorption depth which greatly contributed to a better understanding of the values. geodynamic history of the area. Large Variscan thrusts cutting the During the last 20 yr, the development of national permanent seis- entire pre-Mesozoic basement have been evidenced beneath the mic networks as well as temporary seismic experiments shed light on Celtic Sea and the British Channel (ECORS-BIRP experiment, the crustal structure beneath western Europe (e.g. Yang et al. 2007; Bois et al. 1991; Cloetingh et al. 2013), beneath the Paris basin Verbeke et al. 2012;Luet al. 2018). Those studies focused on cen- near the Bray fault (ECORS experiment, Cazes et al. 1985, 1986), tral Europe (and for a lot of them, the Alps) where seismic stations and in the South-Armorican domain near the SASZ (GeoFrance3-´ coverage is the best. In 2011–2013, temporary networks of broad- D-Armor project, Bitri et al. 2003; Martelet et al. 2004; Bitri et al. band seismometers have been deployed in southwestern France, 2010). Moreover, steeply dipping thrust faults localized in the up- along the French Atlantic coast, and in northern Spain as part of the per crust and related to the Cadomian orogeny were detected in PYROPE (Chevrot & Sylvander 2017)andIBERARRAY (Diaz et al. the North-Armorican domain (GeoFrance3-D-Armor´ project, Bitri 2009) experiments. Using this data set, Chevrot et al. (2014)per- et al. 2001). Active source seismic sounding results tend to support formed a 3-D VP tomography of the upper mantle structures beneath the presence of a relatively flat Moho (average depth of 30 ± 5 km) the Pyrenees and the surrounding regions. The tomography shows beneath the Armorican Massif (Sapin & Prodehl 1973; Matte & negative anomaly beneath the Massif Central and the segmentation Hirn 1988; Bitri et al. 2001, 2003, 2010) and the Paris basin (Cazes of the lithosphere in southwestern France by major faults inherited et al. 1985, 1986). Moreover, it is generally admitted that the Moho from the Variscan orogeny. The VS crustal structure of the Pyrenees is very shallow (<20 km) in the Parentis oceanic basin, located and the surrounding regions was obtained from ambient noise sur- in the heart of the Bay of Biscay (Pinet & Montadert 1987). The face wave tomography (Macquet et al. 2014). The model exhibits magnetic and gravity maps support the hypothesis that the Central- clear seismic signatures correlated with known geological features. and North-Armorican domains belong to the same bounded Six additional broad-band seismic stations have been deployed in 3-D crustal VS model of western France 2175 the western France (Armorican Massif and western part of Parisian 2 DATA PROCESSING Basin) in order to extend the PYROPE network. They strongly con- The seismic data come from a subset of 55 broad-band seismo- tribute to a better resolution of the crustal structures in the targeted logical stations belonging to the previously described temporary region (see black dashed-line rectangle in Fig. 1a). networks and three permanent national networks (RESIF,1 British The synchronous deployments of temporary networks in addition Geological Survey, and Irish National Seismic Network). Fig. 1(b) to the permanent stations available at this time enable to use crustal shows the station locations and technical details are summarized in imaging techniques based on empirical Green’s function computa- the Supplementary Material 1. We used data between September tion from seismic ambient noise cross-correlations (Campillo 2006). 2011 and December 2013 recorded on the vertical component and Surface waves are mainly reconstructed in the cross-correlations filtered between the 2.5 and 50 s period band. The analysis of the in the 1−50 s period range, which makes the seismic ambient horizontal components is beyond the scope of the paper which fo- noise cross-correlation method a powerful tool for crustal imaging cuses on tomography based on vertical component Rayleigh waves. (Shapiro et al. 2005). Most surface wave ambient noise tomography The total of 55 stations corresponds to 1485 interstation pairs, with techniques rely on tracking the maximum of the envelope of the sur- a minimum and maximum path length of 25 km and 1631 km, face wave train filtered around a discrete period in order to find the respectively. group velocity dispersion curve (Levshin et al. 1989). Nevertheless, Downloaded from https://academic.oup.com/gji/article/224/3/2173/5989699 by CNRS user on 15 April 2021 The empirical Green’s function builds up after a sufficient self- the presence of several maxima at each period due to incoherent averaging process which is provided by a random/uniform spa- noise, multipathing and/or waves interference often poses severe tial distribution of the noise sources as well as scattering due to problems to obtain smooth group velocity dispersion curves. Thus, crustal heterogeneities (Campillo 2006). This is achieved by cross- (semi-) manual picking is recommended to prevent misleading re- correlating long time series, since the spatial distribution of the sults (Herrmann 2013). However, dense seismic networks lead to a oceanic noise sources varies with time. In practice, an averaging huge amount of data which severely limits the possibility of a sys- over cross-correlations of single short duration time windows is tematic visual inspection. Therefore, fully automatic methods have usually realized. However, high energetic signals due to short tran- emerged, such as the FTAN (Frequency Time ANalysis) technique sient events (such as earthquakes or oceanic storms) and signals due (Levshin & Ritzwoller 2001;Bensenet al. 2007) which has been to persistent localized source (e.g. Gaudot et al. 2016) can contam- successfully used in many ambient noise tomographic studies. How- inate the cross-correlation results. Therefore, dedicated processing ever, the main disadvantage of such approaches is that ad hoc user’s schemes based on a good knowledge of the regional ambient noise criteria control the degree of smoothness of the dispersion curve. properties must be used to ensure the emergence of unbiased em- Depending on the user’s choices, the resulting dispersion curve may pirical Green’s functions. display either unrealistic jumps or an oversmoothed shape. More- over, the condition of smoothness is satisfied only in a restricted period band, resulting in truncated dispersion curves which poten- tially omit relevant information contained in the full period band. A 2.1 Empirical Green’s function emergence in an further difficulty is the evaluation of dispersion curve uncertainties. ocean-edge context The use of the stability of spatially clustered and temporally re- peated measurements or the use of the signal-to-noise ratio (SNR) The seismic network (Fig. 1b) is surrounded by the North Atlantic as a proxy have been proposed to quantify uncertainties (Bensen ocean, the North sea, the Baltic sea and the , et al. 2007; Nicolson et al. 2014). Most of techniques assume a where active sources of seismic noise occur in the 1–30 s period Gaussian distribution for the data uncertainties, but this approxi- band over the whole year (Friedrich et al. 1998). Furthermore, a mation fails in many cases. For instance, multipathing effects may significant amount of seismic noise coming from eastern Europe > result in a multimodal distribution. Therefore, it remains a challenge has been observed at periods 20 s (Yang & Ritzwoller 2008). The to get the group velocities uncertainties in a robust way. oceanic seismic noise sources in western Europe exhibit a high vari- The contributions of this study are twofold. First, we present ability in space, time and frequency (Chevrot et al. 2007; Beucler a new surface wave inversion approach, which does not require et al. 2015), and thus strong ambient noise emerges from many di- group velocity dispersion picking and does not assume Gaussian rections when considering long durations, even though a dominant uncertainties. Following the idea of Cauchie & Saccorotti (2012) energy coming from the North is clearly observed at < > and Panning et al. (2015), the proposed strategy relies on a Markov periods 10 s (Ermert et al. 2015). At periods 10 s, the seismic chain Monte Carlo (McMC) inversion of the noise cross-correlation noise energy tends to be more isotropic and displays less seasonal variations (Yang & Ritzwoller 2008). Therefore, the noise condi- dispersion diagram for retrieving 1-D VS variations with depth. Sec- tions of the study region are rather favorable for the reconstruction of ondly, we present the first regional 3-D isotropic VS model beneath western France and the surrounding area by combining data from the empirical Green’s function in the 2.5–50 s period band. The low temporary experiments and permanent national seismic stations. level of seismicity of the study area implies that transient energetic This paper is organized as follows. In Section 2, we present the seismic arrivals due to regional and global earthquakes dominate the data processing, with a special emphasis on the regional noise con- spurious signal to remove. In such case, procedures which consist ditions and the pre-processing dedicated to the empirical Green’s in disregarding completely (1-BIT normalization, Campillo & Paul function retrieval. We hereafter present the non-linear McMC in- 2003) or partially (running absolute mean, referred to as RAM, Bensen et al. 2007) the amplitude information of the time series version procedure to get the 1-D path average VS profiles from the noise cross-correlation dispersion diagrams. In Section 4, we go into some details on the regionalization method used to build the 3-D VS model. Finally, the major features of the VS model are discussed and compared to previous geophysical results. 1French permanent network including RLBP,Geoscope and CEA-LDG sta- tions. 2176 I. Gaudot et al. prior to the cross-correlation, are well suited. In the frequency do- teredbetween5speriodandTmax,whereTmax varies for each station- main, spectral whitening is usually applied to reduce the influence pair ensuring that—for a group velocity range of 2–5 km s–1—at of monochromatic signals (Bensen et al. 2007). least three wavelengths can exist within the corresponding intersta- Considering the previous statements, the data processing is or- tion distance (Bensen et al. 2007). The paths associated with Tmax ganized as follows. First, the continuous records at each station < 15 s are discarded to avoid the analysis of too narrow frequency is segmented into non-overlapping 24-hr-long windows. The win- bandwidth empirical Green’s functions. A total of 1268 empirical dows with less than 90 per cent of data are rejected, and the possible Green’s functions out of the 1485 initial cross-correlations data set remaining gaps are linearly interpolated. The data at each station are retained after the SNR and wavelength selection criteria. are then decimated to a uniform sampling rate of 1 Hz using an appropriate anti-aliasing filter. After removing the daily mean and trend, the instrument response is removed in the 2.5–50 s period 3 NON-LINEAR EXPLORATION OF band. Then, the temporal amplitudes are smoothed using a RAM RAYLEIGH GROUP VELOCITY normalization with a normalization window width of 25 s. We tested DISPERSION DIAGRAMS several RAM normalization window widths (5, 11, 17 and 25 s), and the 1-BIT method (i.e. normalization window width equals 1 s). 3.1 Data space Downloaded from https://academic.oup.com/gji/article/224/3/2173/5989699 by CNRS user on 15 April 2021 We found that a width of 25 s (half of the maximum period con- AsshowninFig.4(a), the empirical Green’s function obtained sidered) gives the best results in terms of SNR, and that the 1-BIT by the ambient noise cross-correlation between vertical compo- normalization is significantly less performant than the RAM nor- nent records is dominated by a Rayleigh surface wave dispersive malization. Spectral whitening is then applied, which means that signal. For several reasons such as narrow band filtering side ef- the amplitude spectrum is divided by itself in the 2.5–50 s period fects and/or multipathing, the step which consists in determining band to reach a value of 1, and the other spectral amplitudes are the most likely group velocity curve for a given path, by multiple set to 0. All the synchronous pre-processed 24-hr-long windows filtered envelopes, can be strongly biased. For studies which are us- are then cross-correlated. The daily cross-correlations are stored ing empirical Green’s function as real input waveform, the seismic in the time domain from –3600 to 3600 s. Finally, the available ambient noise properties may also affect the reconstruction qual- single cross-correlations are linearly stacked in the time domain ity which can prevent to reliably pick a continuous group velocity to produce a unique long-term average cross-correlation for each curve over the whole frequency range (e.g. Macquet et al. 2014). station pair. The Fig. 2 shows that most of the cross-correlations On the other hand, for studies which are using deterministic sources displays a clear emergent signal in a time window defined by ar- such as earthquakes, the source frequency can affect if one wants rival times corresponding to typical surface wave group velocities to select the continuous ridge (of a given branch). Some recent im- (grey lines). As expected, the amplitude symmetry of the emergent provements can help to avoid this pitfall (Kol´ınsky´ et al. 2019)but signal in the cross-correlation strongly depends on the station pair the velocity curve variances do not always reflect the complexity orientation. For NW-oriented pairs, the amplitude of the emergent of a real data dispersion diagram. In order (i) to handle the signal signal is higher in positive time lags than in negative time lags. complexity in the time-frequency domain and (ii) to provide reliable For NE-oriented pairs, emergent signals with similar amplitude are uncertainties, we introduce a new approach to explore a dispersion observed at both negative and positive time lags. Moreover, short pe- diagram without picking any group velocity curve. As many other riods dominate the emergent signal for NW-oriented pair compared studies, the input waveform is converted into a dispersion plot by to NE oriented pairs. The empirical Green’s function emergence is using multiple narrow bandpass filters and the station pair distance. evaluated using the SNR, hereafter referred to as SNR. It is defined The novelty of our approach is to consider the whole dispersion as the ratio of the maximum amplitude of the Rayleigh wave to the diagram as the data space. The envelope of each resulting filtered rms amplitude of the noise in a 1000 s time window length, starting waveform is seen as a probability density function (pdf) of possi- 200 s after the Rayleigh wave train. We show in Fig. 3 that the SNR ble group velocity values and the data space is then a collection of strongly depends on the azimuth. The azimuthal distribution of the individual pdf (Fig. 4b). SNR is related to the distribution of the incoming seismic noise energy (Stehly et al. 2006). The polar distribution of SNR shown in Fig. 3 indicates of dominant arrival of seismic noise energy com- 3.2 Non-linear inversion scheme ing from the northwest of the array, which is perfectly consistent with the North Atlantic ocean influence. However, one may also 3.2.1 Inverse procedure framework note that whatever the angle the minimum SNR value is 8. This indicates that although there is a strong noise directivity pattern the The inverse procedure we present in this section has some differ- requirements to reliably reconstruct empirical Green’s functions are ences compared to the classical way of inferring 3-D models. Most fulfilled, mostly thanks to the long duration time-series. of tomographic studies using surface waves (fundamental and/or higher modes) need a stage which is the construction of group/phase velocity maps (Barmin et al. 2001;Sabraet al. 2005;Ekstrom¨ 2011, among many others) to further convert local group/velocities pertur- bations into 1-D models (e.g. Ritzwoller & Levshin 1998; Shapiro 2.2 Selection criteria for empirical Green’s functions et al. 2005; Nishida et al. 2009;Kol´ınsky´ et al. 2014). This step The cross-correlations with a SNR <5 in the causal and anticausal can be made since an ensemble of individual velocity curves are ex- part are rejected to guarantee than the dispersion diagram compu- tracted from the initial waveforms. In our case, we consider that if a tation is performed on emergent Rayleigh wave trains. The selected given waveform (obtained from ambient noise cross-correlation or cross-correlations are symmetrized (that is by stacking their causal from a real earthquake seismogram) is a resultant of the wave field and time-reversed anticausal signals to get a unique signal with a travelling along a given ray path then it might be possible to directly enhanced SNR, see Fig. 4a). The cross-correlations are bandpass fil- infer the probability of all 1-D models that fit the data. In a way, 3-D crustal VS model of western France 2177

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Figure 2. Cross-correlations filtered in the 2.5–50 s period band represented in time-distance plots. (a) Subset of 25 cross-correlations from northwest (N135◦ ± 3.5◦) oriented pairs. The virtual source is the northermost station for each station pair, so that seismic energy propagating from northwest to southeast contributes to the signals in positive lags. (b) Subset of 25 cross-correlations from northeast (N45◦ ± 3.5◦) oriented pairs. The virtual source is the westernmost station for each station pair, so that seismic energy propagating from southwest to northeast contributes to the signals in positive lags. The grey lines indicate linear moveouts of 2 and 5 km s–1. Clear emergent signals with a moveout near 3 km s–1 is observed. Each correlation is normalized relative to its absolute maximum.

ρi this approach has some common points with the partition waveform where D is the intersection value of the theoretical group velocity (Nolet 1990; Lebedev et al. 2005). It means that a given trial 1-D VS dispersion curve computed for a given trial 1-D VS model, and the model can be uniquely turned into a group velocity curve and the fit corresponding individual pdf computed for the period index i in the of this curve in the data space (i.e. the whole dispersion diagram) data space D,wherei = 1,...,nw, with nw is the total number of enables to measure the pertinence (i.e. the likelihood) of the model. narrow bandpass filters. The sum over log values is used to prevent This can be achieved since each group velocity curve intersect the numerical instabilities. Since we consider that individual pdf in the ensemble of group velocity pdf for all frequencies of the dispersion data space may have arbitrary shape, the likelihood formulation in diagram (Fig. 4b). eq. (2) differs from classical methods which rely on a L-norm misfit Following Tarantola (2005), the solution of an inverse problem computation. can be described as the a posteriori pdf σ (m) in the model space M,suchas 3.2.2 Model parametrization and prior on parameters σ ∝ ρ , (m) M (m) L(m) (1) In this study, we infer 1-D VS probabilities for quite long paths (>180 km). Given the depth variability of the strong velocity con- where ρM (m) is a pdf defined in the model space that carries our a trasts expected over the studied area (see Chevrot et al. 2014, for the priori information on models m,andL(m) is the likelihood func- topography of the Moho), velocity gradients rather than discontinu- tion, which gives a measure of how good a model m is in explaining ities are likely to be detected in the path average velocity profiles. the observed data. Assuming the observations to be independent Therefore, we think that a model parametrization that allows both and that modelling uncertainties may be neglected, the likelihood is continuous velocity variations with depth and discontinuities can be defined as well-suited. Following Drilleau et al. (2013), we choose a succes- sion of cubic Bezier´ curves to describe the overall velocity profile nw nw (Fig. 5). Each Bezier´ curve is based on a set of four control points, = ρi = ρi , = L(m) D log( D) (2) noted Pj0, Pj1, Pj2, Pj3,wherej 0,..., N denotes the index of i=1 i=1 2178 I. Gaudot et al.

3.2.3 Bayesian exploration

Thefactthattheaprioriinformation ρM (m) can not be described analytically and that each individual pdf in the data space may exhibit a complex shape with several maxima, a global search method must be used to solve the inverse problem. Therefore, we use a Monte Carlo (MC) approach which does not assume any particular distribution and achieves a global search in the model space. Among others, MC approaches based on the Metropolis– Hastings (MH) algorithm (Metropolis & Ulam 1949; Metropolis et al. 1953; Hastings 1970) are widely used in geophysics (e.g. Tamminen & Kyrol¨ a¨ 2001; Malinverno 2002), especially in seis- mology (e.g. Bodin et al. 2012; Drilleau et al. 2013;Shenet al. 2013). The MH algorithm is used in this study. The MH algo- rithm is an acceptance/rejection algorithm based on a likelihood Downloaded from https://academic.oup.com/gji/article/224/3/2173/5989699 by CNRS user on 15 April 2021 ratio which designs a guided random walk in the model space that samples σ (m). Each iteration involves a 3-steps process: (i) propo- sition, (ii) forward problem and likelihood computation and (iii) acceptance/rejection (Metropolis rule). (i) At the iteration j,anew model m j is generated from a random perturbation of the previ- ous one m j−1 following a proposal distribution f (m j |m j−1). The proposal distribution is often chosen to be symmetric and normally 1 2 2 distributed, that is f (m |m − ) = √ exp(−(m − m − ) /2γ ) j j 1 γ 2π j j 1 Figure 3. Azimuthal distribution of the signal-to-noise ratio (SNR) asso- where γ is the standard deviation of the proposal distribution. (ii) ciated with the cross-correlations filtered in the 2.5–50 s period band (see The forward computation is done to enable the computation of ◦ Fig. 2). The averages SNR values computed over bins of 10 are represented. the likelihood function L(m j ) associated with the proposed new model m j . (iii) The proposed model is accepted with the proba- bility Pa = min[1 , L(m j )/L(m j−1)]. The Metropolis rule permits the curve. Each Bezier´ curve does not pass generally through Pj1 the acceptation of a model which deteriorates the likelihood value, and P which give an information about the curvature according avoiding the issue of converging to local minima. When the pro- j2 −−−→ = − − to the norm and the direction of the tangent vectors Pj0 Pj1 and posed model m j is rejected, m j m j 1 and thus m j 1 is sampled −−−→ again. The resulting walk is called a Markov chain because each new Pj2 Pj3 (Fig. 5a). The continuity between two consecutive curves is provided by identical upward and downward derivatives at each sampled model only depends on the previous model. This Markov junction point. For each curve, P and P are referred to as an- chain statistically converge towards a unique equilibrium distribu- j0 j3 σ chor Bezier´ points. The anchor Bezier´ points are the set of model tion that corresponds to the a posteriori pdf (m), which is the parameters m. The junction points are anchor Bezier´ points which solution to the inverse problem. are common to two consecutive curves. Changing the position of junction points influences the shape of two consecutive curves. 3.2.4 Practical implementation Therefore, the use of more than two Bezier´ curves is needed to de- pict independent variations with depth. This parametrization offers A parallel two-steps inversion scheme is proposed to speed-up the the advantage to describe both smooth and sharp variations with convergence towards the stationary period. During a first step that a minimum number of parameters (see Fig. 5b, for example of VS may be assigned to the burn-in period, a comprehensive exploration profiles described using 6 and 4 anchor Bezier´ points) . of the model space is performed by randomly perturbing the po- The range of possible velocity values is restricted by setting upper sition of all anchor Bezier´ points using wide Gaussian proposal and lower velocity bounds (black lines in Figs 6a–c) based on the distributions. 16 independent Markov chains run in parallel with a range of velocity values observed in the literature (Mooney et al. different number of parameters ranging from 8 (5 anchor Bezier´ 1998; Shapiro & Ritzwoller 2002). A minimal distance of dz = points) to 12 (8 anchor Bezier´ points). The four different parameter 10 km is set between two consecutive anchor Bezier´ points in order configurations are tested on four sets of four chains. The starting to impose a more or less homogeneous distribution of anchor Bezier´ model for each chain is chosen randomly within the prior on pa- points with depth. The depth of each Bezier´ point can be freely taken rameters, and thus each chain follows different paths in the model within the first 100 km. At the top (z = 0 km) and the bottom (z space. Each chain runs over 10 000 iterations. The best-fitting model = 100 km) the depths are set but VS value can be randomly chosen (largest likelihood value) is then determined for each chain. Based within the prior. We force the presence of one anchor Bezier´ point on a comparison of best fit values, an overall selection of 1/4 of –1 at z = 190 km with velocity VS = 4.4 km s given by the PREM the initial Markov chain amount is performed to start the second (Dziewonski & Anderson 1981). No other anchor point can exist step. During the second step, 4 independent chains lasting 30 000 in the 100−190 km depth range. For each cubic Bezier´ curve, the iterations each run in parallel. The sampling of the a posteriori pdf associated control points which define the local tangents and ensure is thus provided by using the four best-fitting models retained at the the continuity are set at a distance of 5 km from the corresponding end of the first step as starting models. At this stage the exploration anchor point. The amount of anchor Bezier´ points (hence the number is performed by modifying only one parameter (VS or depth value) at of Bezier´ curves) varies according to each Markov chain, so that each iteration. This is done with narrower Gaussian proposal distri- the model smoothness is made data adaptive, as in reversible jump butions. The strategy ensures to preserve most of the characteristics McMC methods (Green 1995). of the current model, which may have resulted in a good data fit. 3-D crustal VS model of western France 2179

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Figure 4. Dispersion diagram computation for CLF-E089 station pair. (a) Symmetrized noise cross-correlation computed between CLF and E089 (see Fig. 1b for stations locations). The grey lines indicate arrival times for waves propagating along the great circle interstation path with typical surface wave velocities of 2 and 5 km s–1. (b) Dispersion diagram of the signal presented in (a). At each period, the seismic energy is converted into an individual probability density function (pdf) of the seismic energy (see text for details). The pdfs associated with periods of 6.5 and 28.5 s are shown above in red and green, respectively.

In this inversion scheme, various numbers of anchor Bezier´ points layers with a thickness of 2 km prior to the dispersion curve com- are tested in order not to apriorifix the smoothness of the sam- putation. The choice of 2 km allows to adequately describe both pled velocity profiles. Therefore, we fully benefit of the convenient sharp and smooth variations that may exist in the Bezier´ curves. property of Bayesian inference referred to as ‘natural parsimony’, The choice of layer thickness has no influence on the number of that is preference for the least complex explanation for an observa- model parameters. We only invert for VS since Rayleigh waves tion (MacKay 2003), and in that sense, the algorithm shares some group velocity dispersion measurement are much less sensitive to features with transdimensionnal inversion schemes (Green 1995; VP and density than VS (An & Assumpc¸ao˜ 2005). Therefore, we use Sambridge et al. 2012). The group velocity dispersion curves are a constant VP/VS ratio of 1.73 to compute VP, and we impose that computed using the Thomson–Haskell method (Thomson 1950; density is 3000 kg m–3 for z ≤ 45 km, and 4500 kg m–3 below. The Haskell 1953) in a non-attenuating spherical Earth (CPS Herrmann overall inversion scheme for one 1-D VS profile takes about 10 min 2013). The Bezier´ curves are discretized into a set of homogeneous on a parallel computer system, for a total number of parameters inversed ranging from 8 to 12. 2180 I. Gaudot et al. Downloaded from https://academic.oup.com/gji/article/224/3/2173/5989699 by CNRS user on 15 April 2021

Figure 5. Bezier´ curve model parametrization. (a) Sketch showing 3 Bezier´ curves in blue (B1, top), black (B2, middle) and magenta (B3, bottom). The anchor Bezier´ points are indicated with stars. Other control point and tangent vectors are indicated using black dots and grey segments, respectively. (b) Example of three VS profiles parametrized using 6 (red and green profiles) and 4 anchor Bezier´ points (black profile). The three VS profiles satisfy the prior rule described in Section 3.2.2.

3.2.5 VS a posteriori pdfs depths is unimodal, and tends to be wider as the depth increases. This is the consequence of the decrease of the sensitivity of the Only the samples generated during the second step of the inversion surface wave with depth. The Fig. 6(d) shows that the best fitting are considered to be samples of the a posteriori pdf σ (m). The first sampled models follow the main features of the data. In particu- 5000 samples of each chain are discarded to remove any dependence lar, the bimodal distribution of the seismic energy at short periods on the starting model. The remaining part of the chain is ‘thinned’ clearly appears as a broad distribution at short periods in Fig. 6(e). by keeping 1 iteration over 2, in order to mitigate the covariance When looking at individual random velocity models (in blue in between models. Note that the use of several independent parallel Fig. 6b), it is clear that different families of velocity profiles exist at Markov chains reduces the covariance between models. Finally, shallow depths. The standard deviation of the 100 best-fitting mod- a total of 4 × 12 500 iterations are assembled together to build els (Fig. 6c) carry this peculiarity by providing larger uncertainties the a posteriori pdf, as the one presented in the Fig. 6(a). Next, in the 0–4 km depth range than in the 4–6 km depth range. we compute, for each station pair, a single velocity model with representative uncertainties at each depth. After several test and trials, we found that approximating the a posteriori pdf at each depth as a Gaussian pdf with mean and standard deviation taken 43-DV S MODEL from the 100 best-fitting models (Fig. 6c) is an acceptable choice because it allows us (i) to derive small uncertainties for unimodal 4.1 Tomographic procedure well constrained inversion results in order to favor them in the The tomographic procedure consists in the regionalization, at each subsequent tomographic procedure, (ii) to adequately reflect the depth, of the 1268 V values computed from the MCMC inversion of decrease of surface wave sensitivity with depth. S each noise correlation dispersion diagram. The 3-D velocity model is constructed by gathering 2-D shear wave velocity variations maps computed at each investigated depth from the regionalization. The 3.3 CLF-E089 station pair example regionalization used in this study is a local scale version of the CLF-E089 is a NE–SW oriented station pair with an interstation CLASH (Beucler & Montagner 2006) which has been initially de- distance of 980 km (see Fig. 1b). The Fig. 6 presents the results of veloped for retrieving isotropic and anisotropic seismic velocity the inversion of the empirical Green’s function computed between perturbations at global scales. The method proposed here relies on the stations CLF and E089 (Fig. 4a), once it has been converted into the following assumptions: (i) spherical Earth, (ii) ray theory and a Rayleigh wave group velocity pdfs dispersion diagram (Fig. 4b). (iii) great-circle approximation. Following Backus (1965), we ex-  The group velocity pdfs dispersion diagram shown in Fig. 4(b) is press for the depth z the local azimuthally varying (angle ) VS θ φ somehow noisy and exhibits some complexities, especially at short perturbation at any point of latitude and longitude ,as  periods (5–8 s period band) where a bimodal distribution of the seis- δ θ,φ, , = 1 θ,φ, mic energy is observed. The result of the McMC inversion is the a V ( z ) A1( z) 2V (θ,φ,z) posteriori pdf computed from the accepted velocity model ensem- 0 + A (θ,φ,z)cos2 + A (θ,φ,z) sin 2 ble (Fig. 6a). The a posteriori pdf shows smooth variations of the 2 3  shear-wave velocity with depth. The a posteriori pdf is multimodal + A4(θ,φ,z)cos4 + A5(θ,φ,z) sin 4 , at shallow depths (<4 km) which directly reflects the data com- plexities at short periods. In contrast, the a posteriori pdf at greater (3) 3-D crustal VS model of western France 2181

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(d) (e)

Figure 6. Monte Carlo depth inversion results for the CLF-E089 station pair. (a) a posteriori pdf from the accepted VS model ensemble. (b) 4 best (red) and 20 random (blue) VS models. (c) Mean and standard deviation of the 100 best VS models. (d) Dispersion diagram for CLF-E089 station pair. The group velocity dispersion curves associated with the 4 best and 20 random VS models represented in (b) are plotted in red and blue, respectively. (e) Ensemble of the predicted group velocity dispersion curves associated with the accepted VS models during the inversion procedure, represented in terms of pdf in the data space. In a,b,c, the vertical black lines represent the upper and lower bound VS models, giving the minimum and maximum VS values allowed at each depth.

δ = − β2 where V V V0. V0 is a reference velocity (in our case given ters: the apriorivariance on data ( d ), the apriorivariance on α2 by the median of all path-averaged velocities). A1,...,A5 depend parameters ( p) which constrains the anomaly amplitude, and the on elastic parameters of the medium (Montagner & Nataf 1986; spatial correlation length ( ) which constrains the smoothness of Lev´ equeˆ et al. 1998). Following the conclusions of Trampert & the model parameters (Montagner 1986). Adequate values also Woodhouse (2003) and Beucler & Montagner (2006), we include in ensure that all the model parameters are associated with a sufficient the inversion process the isotropic term (A1) and all the azimuthal number of intersections between paths of various azimuths to solve anisotropic terms (i.e. A2, A3, A4, A5) to prevent artefacts in the the possible non-uniqueness induced by an uneven or an insuffi- results. However, only the isotropic model will be discussed in cient ray path coverage. Since the theoretical errors are assumed this paper. The tomographic problem involves an iterative gradient to be negligible, βd corresponds, for a given station pair, to the a least-squares optimization technique (Tarantola & Valette 1982). posteriori Gaussian standard deviation taken from the 100 best path The question of which starting model to use at each depth has no average VS velocity values retrieved from the McMC inversion of trivial answer. Here, we choose as the starting model a uniform the corresponding noise cross-correlation dispersion diagram (Sec- β2 model with VS value computed from the median of all the 1-D path tion 3). For each depth, the d values are rescaled between 5 and 10 α2 average VS values for a given depth. The model parametrization is per cent, and p is set to 10 and 2 per cent for the isotropic and the based on 999 regularly spaced nodes every 50 km at the spheri- anisotropic components, respectively. The values for the isotropic cal Earth’s surface. The relationship between the data and model and anisotropic terms are set to 75 and 150 km, respectively. These parameters is directly governed by the ray path intersections. The values do not vary with depth because the path coverage is identical inversion for A1, ..., A5 is controlled by three kinds of parame- for each depth. 2182 I. Gaudot et al.

4.2 Resolution analysis displays a large scale strong negative perturbation (–10 per cent) over northwestern part of France. The southwestern part of France The synthetic reconstruction tests are an easy and fast method to exhibits a moderate negative velocity perturbation (–5 per cent). gain insight into the resolution of the tomographic images. The use A localized strong (+10 per cent) positive anomaly is observed of tightly spaced checkerboard test is a common practice in ambient in the Bay of Biscay. The eastern part of France is characterized noise surface-wave tomography. However, as shown by Lev´ equeˆ by a moderate (+5 per cent) positive north–south oriented velocity et al. (1993), this method can be misleading because small-size perturbation centred in the Massif Central. The 30 km depth slice structures may be well retrieved while larger structures are not. Here, (Fig. 8d) exhibits similarities with the results obtained at 16 km, but we follow the conclusions of Rawlinson & Spakman (2016)who the V perturbations are higher (±15 per cent). Central France dis- advocate the use of a synthetic model involving a sparse distribution S plays a strong negative (–15 per cent) anomaly. The Bay of Biscay of spikes. The Fig. 7(a) shows an example of such model. Each spike and surrounding regions is characterized by a large scale positive is a 100×100 km uniform isotropic velocity perturbations of ±10 velocity perturbation, which includes the northeastern part of Spain, per cent with respect to the median velocity value. The synthetic data westernmost part of Brittany, and Cornwall. Moreover, the N–S ori- are calculated using the same forward problem and path coverage ented positive velocity perturbation in southeastern France detected as available for real data analysis. The apriorivariance (β2)on d at 16 km depth persists and covers a broader area. This velocity Downloaded from https://academic.oup.com/gji/article/224/3/2173/5989699 by CNRS user on 15 April 2021 synthetic data is taken from the real data inversion results for the perturbation pattern is observed over the entire Massif Central and depth of 30 km. The same inversion parameters as described in 4.1 it extends further east across the Vosges-Black Forest regions. are used. The only difference is that the azimuthal anisotropy is not taken into account. Fig. 7(b) displays the retrieved model. The shape and the amplitude of the spikes located inland and along the shore in Brittany are well recovered. The slight blurring effect and 5 DISCUSSION the amplitude dampening are likely due to the spatial correlation The most obvious characteristic of the results at 4 km depth (Fig. 8a) between model parameters imposed by the tomography procedure. is the very good correlation of the V perturbations with the sur- On the other hand, the spike located offshore in the Bay of Biscay S face geology (see Fig. 1a for details concerning geological region is not well resolved. The output model exhibits a strong NE–SW names). Indeed, the crystalline Variscanmassifs (Armorican Massif, stretching of the input anomaly, which may be clearly related to the Massif Central, Morvan, the Ardennes Massif, the Vosges, Black- poor azimuthal and intersection path coverage in this area, as shown Forest, Cornwall, Iberian mountains) are characterized by posi- in the Figs 7(c) and (d). tive VS perturbations, whereas Mesocenozoic sedimentary basins of France (Aquitan, Southeastern and Paris basins), Great-Britain (Hampshire Weald basins) and Spain (Basque-Cantabrian, Ebro 4.3 3-D VS model and Duero basins) are associated with negative VS perturbations. The Figs 8(a)–(c) shows the inversion results at 4, 16 and 30 km Our tomographic results delineate the same geological domains depths, respectively. Each depth slice displays local perturbations as recent absorption tomography results computed in the 1–2 Hz of the isotropic VS value with respect to the median VS value for frequency range (Mayor et al. 2017). Interestingly, the strongest each depth (indicated in the lower right of each map). The inversion signals (–7.5 per cent) are located in the Southeastern basin, in the results display smooth lateral velocity variation in the resolved area, Basque-Cantabrian basin, and in the southern part of the Aquitan and the velocity perturbations are null outside the seismic network, basin where the sediment depth is greater than 10 km (Fernandez- which tends to show that developments to use the CLASH at local Mendiola & Garc´ıa-Mondejar 1990; Le Pichon et al. 2010), and scale work. The results become more ‘patchy’ at the border of the where persistent high attenuation regions have been detected by seismic network, especially in the Bay of Biscay where numerous Mayor et al. (2017). In contrast, weaker negative VS perturbations small-scale perturbations are visible. Those small-scale perturba- (–2.5 per cent) are observed in the Paris, Ebro, Duero, Hampshire tions are a logical consequence of the poor path coverage in these and Weald basins, and the northern part of the Aquitan basin where regions. The Fig. 8(d) displays the a posteriori variance on the the sediment filling does not exceed 4 km. In Fig. 9(a), we focus on isotropic parameters computed for the 30 km depth slice result. The the results at 4 km depth in western France and surrounding regions, a posteriori variance is lower than to 5 per cent in the resolved area, after converting the VS perturbations into absolute VS values. hence demonstrating the reliability of the results. The a posteriori Let us assume that Vs < 3.15 km s–1 are associated with variance map barely changes with depth since it is mainly con- Mesocenozoic sedimentary rocks (red-orange colors), and that 3.26 –1 trolled by the path coverage (Fig. 7c), which remains identical for < VS < 4.1 km s characterize crystalline rocks belonging to the each depth in our case. At 4 km depth (Fig. 8a), we observe a large pre-Mesozoic basement (green colours). Following this hypothesis, scale ‘V-shape’ positive perturbation across France. This strong (+4 our results show that the connection between the South-Armorican per cent) perturbation is centred in the Massif Central, and its west- domain and the Massif Central Variscan basement is made beneath ernward and easternward extensions cover the Armorican Massif the Poitou-High along a NW–SE oriented pattern (labelled as ‘PH’ and the Morvan, respectively. Small scale positive perturbations in Fig. 9a). This result is in agreement with geodynamic models of weaker amplitude (+4 per cent) are observed in Vosges, Foret and observations showing that Variscan lithologies of the south- Noire, Belgium, southwestern part of Great Britain (Cornwall), in ern part of the Armorican Massif and the Massif Central are closely the Iberian mountains, in the Alps, and in the eastermost part of the related, with a geometry that follows the NW–SE trend of the South- Pyrenees. Strong negative VS perturbations (–7.5 per cent) are found Armorican Shear Zone (e.g. Baptiste et al. 2016). The VS map also in the southwestern France, Bay of Biscay, southeastern France, and shows that the sediment column thickness might reach 4 km in the northern Spain. The model exhibits weaker negative perturbations eastern part of the Paris basin (‘E’ label). This is in agreement with (–2.5 per cent) in the southern part of Great Britain, and in the centre the asymmetry of the sediment filling of the Paris basin, which and northern part of France. At 16 km depth (Fig. 8b), the veloc- is characterized by a higher sediment thickness in its eastern part ity structure shows significant differences. The 16 km depth slice (Perrodon & Zabek 1990). 3-D crustal VS model of western France 2183 Downloaded from https://academic.oup.com/gji/article/224/3/2173/5989699 by CNRS user on 15 April 2021

Figure 7. Resolution test and path coverage. (a) Input model. (b) Output model. (c) Path coverage in terms of number of intersections. (d) Path coverage in terms of azimuthal coverage score. A score of 4 indicates at least one path in the four quadrants.

At 30 km depth, the tomographic image shows clearly different and that the ocean−continent transition would be located along patterns (Fig. 8c). The positive velocity perturbations in the Bay the French and Spanish Atlantic coastlines. In the Vosges/Massif- of Biscay and in the Vosges/Massif-Central/Southeastern part of Central/Southeastern part of France, our results show a thin crust, France are most likely related to the presence of mantellic mate- in agreement with the recent results of Macquet et al. (2014)and rial. It is known that the Moho is shallow (<20 km) beneath the Chevrot et al. (2014). Those regions would have experienced crustal Parentis basin, in the heart of the Bay of Biscay (Pinet & Mon- thinning due to the Alpine orogeny (Autran et al. 1994). On the tadert 1987). Our results also show that the Moho depth would contrary, the negative anomaly observed in centre and northwestern not exceed 30 km beneath the Armorican and Cantabria shelfs, parts of France could be related to a crustal thickening. In Fig. 9(b), 2184 I. Gaudot et al. Downloaded from https://academic.oup.com/gji/article/224/3/2173/5989699 by CNRS user on 15 April 2021

Figure 8. Isotropic VS perturbations maps at the depths of (a) 4 km, (b) 16 km and (c) 30 km. The median VS value is indicated in lower right of each map. The dashed black rectangle in (a) indicates the western France and the surrounding regions. The main geolocical features of the region are indicated. See Fig. 1(a) for legend. (d) a posteriori variance on model parameters associated with the 30 km depth result. we focus on the results at 30 km depth in western France and sur- of crustal material covering a large area in the northwestern part rounding regions, after converting the VS perturbations into absolute of France (labelled as ‘Z1’, ‘Z2’, ‘Z3’, ‘Z4’ in Fig. 9b). This low VS values. velocity area seems to be limited in the East by the Paris Basin Mag- –1 Let us assume that 3.8 < VS < 3.9 km s are associated with netic Anomaly (PBMA, eastern boundaries of ‘Z3’ and ‘Z4’) and –1 lower crust material, and that VS > 4.1 km s characterize mantel- in the South by the South-Armorican Shear Zone (SASZ) (south- lic rock. Following this hypothesis, our results show four regions ern boundaries of ‘Z2’ and‘Z3’). In the Armorican Massif, the 3-D crustal VS model of western France 2185 Downloaded from https://academic.oup.com/gji/article/224/3/2173/5989699 by CNRS user on 15 April 2021

Figure 9. Isotropic VS horizontal and vertical cross-section in the 3-D model for western France and the surrounding regions. (a) 4 km horizontal cross-section. The position of the vertical cross-section presented in (c) is indicated with A and B. The position of the ECORS profile (Matte & Hirn 1988) is indicated with 1 and 2. (b) 30 km horizontal cross-section. See Fig. 1(a) for legend. Labelled white rectangles indicate specific features discussed in the text. (c) Vertical cross-section at –1◦ longitude between 45◦ and 50◦ latitude. The continuous black lines superimposed on the section report the Moho depth detected along the ECORS profile. The red rectangle indicates the area between the cities of Thouarce´ and Le Mans where anomalous reflectivity and attenuation pattern have been detected(Matte & Hirn 1988; Campillo & Plantet 1991). See text for details. southern boundary of this low velocity area follows the northern Plantet (1991) and Matte & Hirn (1988), respectively. The verti- branch of the SASZ (southern boundary of ‘Z2’). Further East, this cal cross-section shown in Fig. 9(c), along with the Moho depths low velocity area is limited to the South by the southern branch of detected on the ECORS seismic profile from either side of this the SASZ and by the Nort-sur-Erdre (NSE) fault (southern bound- area (Matte & Hirn 1988) supports the hypothesis of crustal thick- ary of ‘Z3’). The northward extension of this area is less clear, but it ening. Following the geodynamic models proposed by Ballevre` could be limited by the Rheic suture (northern boundaries of ‘Z1’, et al. (2009), the large area encompassing ‘Z1’, ‘Z2’, ‘Z3’ and ‘Z2’ and ‘Z4’). The region ‘Z2’ crosses the Central-Armorican ‘Z4’ could be associated with the deep crustal root of the Armorica domain in a vicinity of a zone where strong seismic attenuation and microplate whose southern and eastern boundaries are the SASZ anomalous reflectivity pattern have been revealed by Campillo & and the PBMA, respectively. Therefore, our results are in line with 2186 I. Gaudot et al. the hypothesis that both SASZ and the PBMA are major crustal to build a permanent antenna of 200 broad-band stations deployed boundaries which could be related to Variscan sutures. However, homogeneously over the metropolitan France will certainly allow to the presence in our tomographic model of two high velocity area improve the knowledge of the deep structures beneath France. in northwestern France (labels ‘L’ and ‘Q’) are more difficult to interpret. The ‘L’ area covers the westernmost part of the Central- and North-Armorican domain, and its eastern boundary does not ACKNOWLEDGEMENTS follow a known discontinuity. We speculate that this high velocity This work is supported by the Regional Council of Pays de la Loire domain could be related to the Leon´ Domain, which is interpreted (VIBRIS project), the French National Research Agency (PYROPE as a microcontinent in some geodynamic models (Ballevre` et al. project ANR-09-0229-000) (Chevrot & Sylvander 2017), and by 2009;Faureet al. 2010), but further investigations are needed to the Nantes Atlantique Observatory (OSUNA). The temporary ex- confirm this hypothesis. The ‘Q’ area, which is located in the east- periment data sets are referred as DOI:10.15778/RESIF.X72010 ernmost part of the North-Armorican domain and connected with and DOI:10.7914/SN/IB. The authors thank Olivier Quillard and high velocity area in southern Great-Britain, does not correlate, to Pierrick Gernignon for the installation and maintenance of the seis- the best of our knowledge, with a documented feature. Interestingly, mic stations in western France. The authors would like to thank the vertical cross-section shown in Fig. 9(c) indicates that this area Sebastien´ Chevrot, Mathieu Sylvander and all the PYROPE working Downloaded from https://academic.oup.com/gji/article/224/3/2173/5989699 by CNRS user on 15 April 2021 is associated with high velocities down to the mantle. Finally, we group. Wethank Mario Ruiz for preparing and providing IBERARRAY note that there is no evidence for a seismic signature of the Sillon data. IBERARRAY is a contribution of the Team Consolider-Ingenio Houiller which can sometimes be interpreted as a sharp boundary 2010 TOPO-IBERIA(CSD2006-00041) (Institute Earth Sciences between lithospheric domains. ‘Jaume Almera’ CSIC ICTJA 2007). Data from the French per- manent stations are freely available through the RESIF data portal (http://www.resif.fr). The authors would like to thank Sergei Lebe- 6 CONCLUSION dev for providing continuous records from the irish stations. The authors thank Thomas Bodin, Valerie´ Maupin and Martin Schim- The analysis of 2 yr of continuous seismic signals recorded at 55 mel for fruitful discussions. All figures were produced by the GMT broad-band stations located in France and in the surrounding coun- graphic software (Wessel et al. 2019). Seismological data process- tries allowed us to perform the first 3-D crustal regional VS tomog- ing have been mainly done using the ObsPy library (Beyreuther raphy focused on the western France and surrounding regions. The et al. 2010) and SAC program (Goldstein & Snoke 2005). We thank 1-D VS variations with depth are computed from the inversion of Petr Kol´ınsky´ for his very constructive and careful review. Con- Rayleigh wave ambient noise cross-correlation waveform, once it structive remarks by L. Boschi and an anonymous reviewer also is converted into probability density functions of Rayleigh wave helped improving this manuscript. group velocity dispersion. A Markov chain Monte Carlo inversion procedure allows to infer a posterior probability of VS profiles which are turned into a mean 1-D path averaged VS model with standard REFERENCES deviation. This depth inversion strategy has the advantage of not An, M. & Assumpc¸ao,˜ M.S., 2005. Effect of lateral variation and model requiring group velocity dispersion picking, and to provide mean- parameterization on surface wave dispersion inversion to estimate the average shallow structure in the Parana´ Basin, J. Seismol., 9(4), 449–462. ingful uncertainties of the VS with depth. The data coverage enables Arroucau, P., Mocquet, A. & Vacher, P., 2006. 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